In solids, a number of energy bands exist. These energy bands include a valence band and a conduction band. The conduction band is at higher energy than the valence band. Each energy band contains multiple states in which a charged carrier (electron or hole) may be present. In semiconductors and insulators, the conduction band is separated from the valence band by a bandgap. There are essentially no states in the bandgap.
In semiconductors and insulators, at zero temperature and under no excitation conditions, the states in the valence band are completely populated by electrons, while the states in the conduction band are completely populated by holes, i.e. empty of electrons. In metals, on the other hand, the conduction band and the valence band are the same. Thus, metals are highly conductive as electrons are essentially free to move around from a populated state to an unpopulated state. Ideally, in insulators or undoped semiconductors, on the other hand, the conductivity is relatively low because the electrons completely populate the valence band and thus no states are available to which the electrons are able to move. However, there is a finite conductivity in insulators or undoped semiconductors due to thermal excitation. Some of the electrons in the valence band receive enough energy to transition across the bandgap. Once the electrons are in the conduction band, they can conduct electricity, as can the hole left behind in the valence band. As the bandgap increases, the conductivity decreases exponentially. Thus, the bandgap is zero in a metal as the conduction band and valence band overlap, the bandgap is greater than about 4 eV in insulator (e.g. 8.0 eV for SiO2), and between zero and about 4 eV in a semiconductor.
Energy bands are shown in momentum space. That is, the energy bands of a solid are illustrated in terms of the relationship between the available states in energy and momentum. Other constructs are useful in characterizing solids. For example, in solid-state physics a Fermi surface is often used to describe various aspects of a solid. A Fermi surface is an abstract boundary or interface useful for characterizing and predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and semiconductors. The Fermi surface is related to the periodicity of a lattice that forms a crystalline solid (i.e. the distance between elements forming the lattice) and to the occupation of electron energy bands in such materials. The Fermi surface defines a surface of constant energy in momentum space. The Fermi surface, at absolute zero, separates the unfilled states from the filled states. The electrical properties of the material are determined by the shape of the Fermi surface, because the current is due to changes in the occupancy of states near the Fermi surface.
Many electronic and other devices use metals, insulators, and semiconductors. One example of such a device includes a current source. A current source is a device that supplies substantially a constant amount of current independent of the voltage across its terminals. An ideal current source produces the voltage used to maintain a specified current. Many electronic devices use circuit arrangements that contain current sources.
Skilled artisans appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale.